Journal of Applied Mathematics and Informatics, Volume (26), No (2), Year (2008-9) , Pages (213-222)

Title : ( A PRECONDITIONER FOR THE LSQR ALGORITHM )

Authors: داوودخجسته سالکویه , Faezeh Toutounian Mashhad ,

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Iterative methods are often suitable for solving least squares problems min|Ax − b|2, where A 2 Rm×n is large and sparse. The well known LSQR algorithm is among the iterative methods for solving these problems. A good preconditioner is often needed to speedup the LSQR convergence. In this paper we present the numerical experiments of applying a well known preconditioner for the LSQR algorithm. The preconditioner is based on the ATA-orthogonalization process which furnishes an incomplete upper-lower factorization of the inverse of the normal matrix ATA. The main advantage of this preconditioner is that we apply only one of the factors as a right preconditioner for the LSQR algorithm applied to the least squares problem min|Ax − b|2. The preconditioner needs only the sparse matrix-vector product operations and significantly reduces the solution time compared to the unpreconditioned iteration. Finally, some numerical experiments on test matrices from Harwell-Boeing collection are presented to show the robustness and efficiency of this preconditioner.

Keywords

, Least squares problem, the LSQR algorithm, preconditioner, iterative
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@article{paperid:1009131,
author = {داوودخجسته سالکویه and Toutounian Mashhad, Faezeh},
title = {A PRECONDITIONER FOR THE LSQR ALGORITHM},
journal = {Journal of Applied Mathematics and Informatics},
year = {2008},
volume = {26},
number = {2},
month = {September},
issn = {1598-5857},
pages = {213--222},
numpages = {9},
keywords = {Least squares problem; the LSQR algorithm; preconditioner; iterative methods},
}

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%0 Journal Article
%T A PRECONDITIONER FOR THE LSQR ALGORITHM
%A داوودخجسته سالکویه
%A Toutounian Mashhad, Faezeh
%J Journal of Applied Mathematics and Informatics
%@ 1598-5857
%D 2008

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